The Rangers' Matt Rempe, top, fights with the Islanders' Matt Martin...

The Rangers' Matt Rempe, top, fights with the Islanders' Matt Martin during the first period of an NHL Stadium Series game at MetLife Stadium on Feb. 18. Credit: AP/Seth Wenig

GREENBURGH – Matt Rempe is appreciative of all the love and the support he is getting right now, but the 21-year-old Rangers forward is determined not to let his 15 minutes of fame go to his head.

“I'm five games into my career,’’ Rempe said to the horde of reporters surrounding him after practice Tuesday. “I’ve got a long, long way to go. I'm trying to get better every day. Gotta put the work in. I want to show that I can play with skill, play hard, and play it any way. Play multiple ways. Play multiple positions, and be a good player and help this team win games.’’

Rempe, the 6-8, 245-pounder from Calgary, became the first player in NHL history to make his debut in an outdoor game when he played in the Rangers' 6-5 win over the Islanders in the Stadium Series at MetLife Stadium Feb. 18 on the sixth anniversary of his father’s death. Since then, he has become quite the sensation. He has three fights in his first five games and even has a game-winning goal against the Flyers and an assist.

All of his fights have been wildly entertaining bouts with little defense and plenty of haymakers being thrown around by the combatants. He has  fought the Islanders’ Matt Martin, the Flyers’ Nicolas Deslauriers and, most recently, Mathieu Olivier of the Columbus Blue Jackets, who ended the Rangers’ 10-game winning streak on Sunday. The teams meet again Wednesday at Madison Square Garden.

But as he sat at his locker sporting a huge black eye Tuesday, Rempe insisted he’s not allowing himself to get caught up in Rempe-mania.

“I'm just trying to stay off all media,’’ he said. “I’ve got to focus on what got me here, and continue to do that … I'm just trying to keep a level head and just trying to stay down to earth.’’

Rempe said he did enjoy taking photos with fellow patrons at the Cheesecake Factory Monday, but for the most part he’s just happy to go back to his hotel and read his fantasy novels, talk to his mother and sisters, and play his guitar. The calm, soft-spoken way Rempe is dealing with his new celebrity status comes as no surprise to his junior hockey coach with the Seattle Thunderbirds, Matt O’Dette.

“I think that's kind of quite common for tough guys,’’ O’Dette said of Rempe’s quiet nature. “You’d be surprised at the personality off the ice, but I think with the fighting part, it's just another tool in his toolbox. People don't understand yet that this this kid is a pretty good player. A kid that can skate really well for his size; he's got good hands around the net, he's a very smart player.’’

Rempe, who had six goals, 10 points and 87 penalty minutes in 53 games for AHL Hartford in his first pro season last year, had eight goals, 12 points and 96 penalty minutes in 48 games this season before he was called up Feb. 16. In junior hockey, he was more of a well-rounded player with 17 goals in 56 games in his last year of junior, and added eight goals in 24 playoff games as his team made it to the finals of the Western Hockey League.

“When he played for us, he contributed in so many ways,’’ O’Dette said. “And I think, in his WHL career, he only maybe fought eight times total. It's just one of those things where, when he got into his first fight, it was like, 'Oh, wow, I'm good at this.' So this became another tool in the toolbox and something that he could add to his game.’’

Rangers coach Peter Laviolette, who developed a liking for Rempe in the preseason, said Rempe and fellow Hartford call-up Adam Edstrom bring a certain energy to the team.

“[Rempe's] a big guy. He skates hard on the forecheck, he's banged a lot of bodies for us,’’ Laviolette said. “His line [with the 6-7 Edstrom and center Barclay Goodrow], on many occasions has put it behind the defense turned pucks over; brought pucks to the net and scored goals. For the amount of time that they're getting [Rempe has averaged four minutes of ice time in five games], they've produced a couple goals in the last couple of games. And so I think that they've done a good job and yeah, I do think that they've been bringing energy … they've had positive influences on the game.’’

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